Robust H_∞ control of uncertain systems with two additive time-varying delays

This paper is concerned with the problem of delay-dependent robust H_∞ control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H_∞ stability criteria are derived in terms of linear matrix inequalities (LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.